A TQFT from quantum Teichm\"uller theory
J{\o}rgen Ellegaard Andersen, Rinat Kashaev
TL;DR
This paper constructs a new family of topological quantum field theories using quantum Teichmüller theory, expanding the mathematical framework for 3-manifold invariants.
Contribution
It introduces a one-parameter family of TQFTs derived from quantum Teichmüller theory, linking quantum geometry with topological quantum field theories.
Findings
Established a new class of TQFTs from quantum Teichmüller theory
Defined admissible leveled shaped 3-manifolds for the construction
Provided a categorical framework for these TQFTs
Abstract
By using quantum Teichm\"uller theory, we construct a one parameter family of TQFT's on the categroid of admissible leveled shaped 3-manifolds.
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